In this paper we prove that a strictly convex Alexandrov solution u of the Monge-Amp\`ere equation, with right hand side bounded away from zero and infinity, is W2,1loc. This is obtained by showing higher integrability a-priori estimates for D2u, namely D2u∈LlogkL for any k∈N
Abstract. We obtain boundary Hölder gradient estimates and regularity for solutions to the lineariz...
We establish interior estimates for Lp-norms, Orlicz norms, and mean oscillation of second derivativ...
Abstract. It is well-known that the Dirichlet problem for the Monge-Ampère equation detD2u = µ in a...
In this paper we prove that a strictly convex Alexandrov solution u of the Monge-Amp\`ere equation, ...
Abstract. In this paper we prove that a strictly convex Alexandrov solution u of the Monge-Ampère e...
Abstract. In this note we prove that, if the cost function satisfies some necessary structural con-d...
Abstract. We prove that solutions to the Monge-Ampère inequality detD2u ≥ 1 in Rn are strictly conv...
Abstract. We demonstrate that C2,α estimates for the Monge-Ampère equation depend in a highly nonli...
In this note we prove that, if the cost function satisfies some necessary structural conditions and ...
Abstract. We study the properties of generalized solutions to the Monge– Ampère equation detD2u = ν...
In this paper, we establish the global C2,α and W2,p regularity for the Monge-Ampère equation detD2u...
Abstract. Let : Rn! R be a function strictly convex and smooth, and = det D2 is the Monge-Amp `er...
We consider Monge-Ampére equations with the right hand side function close to a constant and from a ...
This thesis contains the author's results on singular solutions to the Monge-Ampere equation \det D^...
Abstract. We study interior C1,α regularity of viscosity solutions of the par-abolic Monge-Ampére e...
Abstract. We obtain boundary Hölder gradient estimates and regularity for solutions to the lineariz...
We establish interior estimates for Lp-norms, Orlicz norms, and mean oscillation of second derivativ...
Abstract. It is well-known that the Dirichlet problem for the Monge-Ampère equation detD2u = µ in a...
In this paper we prove that a strictly convex Alexandrov solution u of the Monge-Amp\`ere equation, ...
Abstract. In this paper we prove that a strictly convex Alexandrov solution u of the Monge-Ampère e...
Abstract. In this note we prove that, if the cost function satisfies some necessary structural con-d...
Abstract. We prove that solutions to the Monge-Ampère inequality detD2u ≥ 1 in Rn are strictly conv...
Abstract. We demonstrate that C2,α estimates for the Monge-Ampère equation depend in a highly nonli...
In this note we prove that, if the cost function satisfies some necessary structural conditions and ...
Abstract. We study the properties of generalized solutions to the Monge– Ampère equation detD2u = ν...
In this paper, we establish the global C2,α and W2,p regularity for the Monge-Ampère equation detD2u...
Abstract. Let : Rn! R be a function strictly convex and smooth, and = det D2 is the Monge-Amp `er...
We consider Monge-Ampére equations with the right hand side function close to a constant and from a ...
This thesis contains the author's results on singular solutions to the Monge-Ampere equation \det D^...
Abstract. We study interior C1,α regularity of viscosity solutions of the par-abolic Monge-Ampére e...
Abstract. We obtain boundary Hölder gradient estimates and regularity for solutions to the lineariz...
We establish interior estimates for Lp-norms, Orlicz norms, and mean oscillation of second derivativ...
Abstract. It is well-known that the Dirichlet problem for the Monge-Ampère equation detD2u = µ in a...
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